A Probabilistically Checkable Proof of Proximity (PCPP) for a linear code $C$, enables to determine very efficiently if a long input $x$, given as an oracle, belongs to $C$ or is far from $C$.PCPPs are often a central component of constructions of Probabilistically Checkable Proofs (PCP)s [Babai et al. ...
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We study *interactive oracle proofs* (IOPs) (Ben-Sasson, Chiesa, Spooner '16), which combine aspects of probabilistically checkable proofs (PCPs) and interactive proofs (IPs). We present IOP constructions and general techniques that enable us to obtain tradeoffs in proof length versus query complexity that are not known to be achievable via PCPs ...
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The seminal result that every language having an interactive proof also has a zero-knowledge interactive proof assumes the existence of one-way functions. Ostrovsky and Wigderson (ISTCS 1993) proved that this assumption is necessary: if one-way functions do not exist, then only languages in BPP have zero-knowledge interactive proofs.

An $r$-simple $k$-path is a {path} in the graph of length $k$ thatpasses through each vertex at most $r$ times. The \simpath{r}{k}problem, given a graph $G$ as input, asks whether there exists an$r$-simple $k$-path in $G$. We first show that this problem isNP-Complete. We then show ...
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We describe new constructions of error correcting codes, obtained by "degree-lifting" a short algebraic geometry (AG) base-code of block-length $q$ to a lifted-code of block-length $q^m$, for arbitrary integer $m$. The construction generalizes the way degree-$d$, univariate polynomials evaluated over the $q$-element field (also known as Reed-Solomon codes) are "lifted" ...
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Let $F$ be the field of $q$ elements, where $q=p^{\ell}$ for prime $p$. Informally speaking, a polynomial source is a distribution over $F^n$ sampled by low degree multivariate polynomials. In this paper, we construct extractors for polynomial sources over fields of constant size $q$ assuming $p \ll q$.

Let $\F$ be the field of $q$ elements. An \emph{\afsext{n}{k}} is a mapping $D:\F^n\ar\B$such that for any $k$-dimensional affine subspace $X\subseteq \F^n$, $D(x)$ is an almost unbiasedbit when $x$ is chosen uniformly from $X$.Loosely speaking, the problem of explicitly constructing affine extractors gets harder as $q$ gets ...
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In this paper we construct explicit deterministic extractors from polynomial sources, namely from distributions sampled by low degree multivariate polynomials over finite fields. This naturally generalizes previous work on extraction from affine sources (which are degree 1 polynomials). A direct consequence is a deterministic extractor for distributions sampled by polynomial ...
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An $(n,k)$-bit-fixing source is a distribution $X$ over $\B^n$ such that there is a subset of $k$ variables in $X_1,\ldots,X_n$ which are uniformlydistributed and independent of each other, and the remaining $n-k$ variablesare fixed. A deterministic bit-fixing source extractor is a function $E:\B^n\ar \B^m$ which on ...
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An $(n,k)$-affine source over a finite field $F$ is a randomvariable $X=(X_1,...,X_n) \in F^n$, which is uniformlydistributed over an (unknown) $k$-dimensional affine subspace of $F^n$. We show how to (deterministically) extract practically allthe randomness from affine sources, for any field of size largerthan $n^c$ (where ...
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